Geometry is a significant part of the Quantitative Aptitude section in the SSC CGL exam. Below are some typical geometry questions that you might encounter in the exam, along with explanations:

### Questions

**The perimeter of a rectangle is 48 cm. If the length of the rectangle is twice its breadth, find the length and the breadth.****In a right-angled triangle, the hypotenuse is 10 cm, and one of the sides is 6 cm. Find the length of the other side.****The area of a circle is 154 cm². Find its radius. (Use π = 22/7)****Find the area of a triangle with a base of 8 cm and a height of 5 cm.****Two circles with radii 7 cm and 3 cm touch externally. Find the distance between their centers.****In a rhombus, the lengths of the diagonals are 16 cm and 12 cm. Find the area of the rhombus.****Find the length of the side of an equilateral triangle whose perimeter is 18 cm.**

### Solutions

**The perimeter of a rectangle is 48 cm. If the length of the rectangle is twice its breadth, find the length and the breadth.**Let’s denote the breadth as $b$ and the length as $l$. Given $l=2b$.

The perimeter $P$ of a rectangle is given by:

$P=2(l+b)$Substituting the given values:

$48=2(2b+b)$Simplifying:

$48=2(3b)$ $48=6b$ $b=8cm$Since $l=2b$:

$l=2×8=16cm$So, the length is 16 cm and the breadth is 8 cm.

**In a right-angled triangle, the hypotenuse is 10 cm, and one of the sides is 6 cm. Find the length of the other side.**Let the other side be $x$. Using the Pythagorean theorem:

$x_{2}+_{2}=1_{2}$ $x_{2}+36=100$ $x_{2}=64$ $x=8cm$The length of the other side is 8 cm.

**The area of a circle is 154 cm². Find its radius. (Use π = 22/7)**The area $A$ of a circle is given by:

$A=πr_{2}$Substituting the given values:

$154=722 r_{2}$Solving for $r_{2}$:

$154×227 =r_{2}$ $r_{2}=49$ $r=7cm$The radius is 7 cm.

**Find the area of a triangle with a base of 8 cm and a height of 5 cm.**The area $A$ of a triangle is given by:

$A=21 ×base×height$Substituting the given values:

$A=21 ×8×5$ $A=20cm_{2}$The area of the triangle is 20 cm².

**Two circles with radii 7 cm and 3 cm touch externally. Find the distance between their centers.**When two circles touch externally, the distance between their centers is the sum of their radii:

$Distance=7+3=10cm$The distance between their centers is 10 cm.

**In a rhombus, the lengths of the diagonals are 16 cm and 12 cm. Find the area of the rhombus.**The area $A$ of a rhombus is given by:

$A=21 ×diagonal_{1}×diagonal_{2}$Substituting the given values:

$A=21 ×16×12$ $A=96cm_{2}$The area of the rhombus is 96 cm².

**Find the length of the side of an equilateral triangle whose perimeter is 18 cm.**Let the side of the equilateral triangle be $a$. The perimeter $P$ of an equilateral triangle is given by:

$P=3a$Substituting the given value:

$18=3a$ $a=6cm$The length of the side of the equilateral triangle is 6 cm.

### Practice Problems

- The perimeter of a square is 64 cm. Find its area.
- The sides of a triangle are 7 cm, 24 cm, and 25 cm. Is it a right-angled triangle? If yes, find the area.
- A circular park has a circumference of 44 m. Find its diameter. (Use π = 22/7)
- The base of a parallelogram is 10 cm, and the height is 6 cm. Find its area.
- In a triangle, the lengths of two sides are 5 cm and 12 cm. The length of the third side is 13 cm. Find the area of the triangle.

These questions cover various aspects of geometry that are commonly tested in the SSC CGL exam. Regular practice will help in mastering these concepts and performing well in the exam.